How much water does is hold? Generally, I find tanks with horizontal space are better than those with vertical space because they allow more room to swim and more air to breath. You should definitely add a hiding place for him.

Very pretty fish!
A few things, does it hold at least a gallon? If so your fine just will need 1 50% and 1 100% change a week. Goes for anything under 5 gallons.
I don't see a heater. Depending on location and room temp you may not need it. If the water is under 76 degrees then he needs a heater. His fins should also spread out more as he gets warmer. A cave or something would be a good idea. There are lots of options some cheaper than others. A good one is a tera cota pot. Just make sure to clean it well, coffee mugs, shot glasses I have seen all of those used.
I would also fill the tank up higher give him more space to swim. The water is just a little to low.

Hi :)
Nice fish!! I have a 3gallon tank like this, it's taller than it is long. My fish Bowser likes to go up and down in it. BUT it's important to add lots of silk plants so he can rest close to the top. And he needs a hiding place. The dollar store here sells cheap coils of silk leaves for decoration (and the stem bends) so I bunch it up and sink it in the tank for multiple levels (it creates somewhere to hide, explore, rest on).
I second the heater thing. Unless your fish water is naturally like 76-78 F then you don't. But I see his fins are kind of clamped here, indicating either stress from his new home and no where to hide or because the water might be too cold.
Welcome to the world of fish keeping!! :)

Personally I think it is too small. My guess is it holds 1 gallon. A Betta can live in that but will not thrive. 2.5 gal is the least a Betta should have IMO but I prefer at least 5 gal if possible.

Don't forget bettas need a heater... :/ I have a Betta in a 10 gal. filtered tank. She is very active with all that room and I get to have fun decorating the whole thing with beautiful live plants! :D walmart has a 10 gal starter kit for $30

It's a good setup, only thing you're missing is a heater because bettas are tropical fish and they doo better in water between 76 and 80.
I've also noticed that my fish love when there's plenty of plants and places to hide, so don't hesitate to put more.